//Group G is generated by
//c2c7(1 5 4)(2 3 7)
//c1c3c5c6c7c9(1 3)(2 4)(5 7)(8 9)
//c2c6(1 4 6 2 3 5 6 7)
//c8c9


5.C7:C12
MatrixGroup(11, Integer Ring) of order 2^2 * 3 * 7
Generators:

    c2c7(1 5 4)(2 3 7)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    c1c3c5c6c7c9(1 3)(2 4)(5 7)(8 9)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 3  1  1  0  1  0  1  1  1  1  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
    [-1  0  0  0  0  0  0  0  0 -1  0]

    c2c6(1 4 6 2 3 5 6 7)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
    
    c8c9
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  0  0  0  1  1]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [-1  0  0  0  0  0  0  0  0 -1  0]
    [-1  0  0  0  0  0  0  0  0  0 -1]
1
{@
    Mod: ( 0  1 -1  0  0  0  0  0  0  0  0),
    Mod: (0 0 0 0 0 0 0 0 1 0 0),
    Mod: (0 0 0 0 0 0 1 0 0 0 0),
    Mod: ( 0  1  0  0 -1  0  0  0  0  0  0),
    Mod: (0 0 0 0 1 0 0 0 0 0 0),
    Mod: (0 0 0 1 0 0 0 0 0 0 0),
    Mod: ( 0  1  0  0  0  0  0  0 -1  0  0),
    Mod: (0 0 0 0 0 0 0 1 0 0 0),
    Mod: (0 0 1 0 0 0 0 0 0 0 0),
    Mod: ( 0  1  0  0  0  0 -1  0  0  0  0),
    Mod: ( 0  1  0 -1  0  0  0  0  0  0  0),
    Mod: ( 0  1  0  0  0 -1  0  0  0  0  0),
    Mod: (0 0 0 0 0 1 0 0 0 0 0),
    Mod: ( 0  1  0  0  0  0  0 -1  0  0  0)
@}
Intersection Matrix:
[-1  0  0  0  0  0  0  0  1  0  0  0  0  0]
[ 0 -1  0  0  0  0  1  0  0  0  0  0  0  0]
[ 0  0 -1  0  0  0  0  0  0  1  0  0  0  0]
[ 0  0  0 -1  1  0  0  0  0  0  0  0  0  0]
[ 0  0  0  1 -1  0  0  0  0  0  0  0  0  0]
[ 0  0  0  0  0 -1  0  0  0  0  1  0  0  0]
[ 0  1  0  0  0  0 -1  0  0  0  0  0  0  0]
[ 0  0  0  0  0  0  0 -1  0  0  0  0  0  1]
[ 1  0  0  0  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  1  0  0  0  0  0  0 -1  0  0  0  0]
[ 0  0  0  0  0  1  0  0  0  0 -1  0  0  0]
[ 0  0  0  0  0  0  0  0  0  0  0 -1  1  0]
[ 0  0  0  0  0  0  0  0  0  0  0  1 -1  0]
[ 0  0  0  0  0  0  0  1  0  0  0  0  0 -1]
Stabilizer Group Name:
C6
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  0  0  0  0  1  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  0  0  0  1  1]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [-1  0  0  0  0  0  0  0  0 -1  0]
    [-1  0  0  0  0  0  0  0  0  0 -1]
2
{@
    Mod: (0 0 0 0 0 0 0 0 0 0 1),
    Mod: ( 0  1  0  0  0  0  0  0  0  0 -1),
    Mod: (0 0 0 0 0 0 0 0 0 1 0),
    Mod: ( 0  1  0  0  0  0  0  0  0 -1  0)
@}
Intersection Matrix:
[-1  1  0  0]
[ 1 -1  0  0]
[ 0  0 -1  1]
[ 0  0  1 -1]
Stabilizer Group Name:
C7:C3
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  1  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]